This question is similar to your earlier one about catching .NET exceptions in JavaScript, and our answer is similar as well - consider catching the exception in JavaScript and allowing .NET code to inspect it. For example:

Is there any plan to have more seamless exception handling between .NET and JS, even for V8 only?

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Currently there's no plan beyond adding a script-callable tryCatch() function on the host side. Generally we favor keeping the engine APIs uniform, but we agree that this may be worth doing anyway, so we've put it on our long-term to-do list.